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25 Zeta and Related FunctionsComputation

§25.19 Tables

  • Abramowitz and Stegun (1964) tabulates: ζ(n), n=2,3,4,, 20D (p. 811); Li2(1x), x=0(.01)0.5, 9D (p. 1005); f(θ), θ=15(1)30(2)90(5)180, f(θ)+θlnθ, θ=0(1)15, 6D (p. 1006). Here f(θ) denotes Clausen’s integral, given by the right-hand side of (25.12.9).

  • Morris (1979) tabulates Li2(x)25.12(i)) for ±x=0.02(.02)1(.1)6 to 30D.

  • Cloutman (1989) tabulates Γ(s+1)Fs(x), where Fs(x) is the Fermi–Dirac integral (25.12.14), for s=12,12,32,52, x=5(.05)25, to 12S.

  • Fletcher et al. (1962, §22.1) lists many sources for earlier tables of ζ(s) for both real and complex s. §22.133 gives sources for numerical values of coefficients in the Riemann–Siegel formula, §22.15 describes tables of values of ζ(s,a), and §22.17 lists tables for some Dirichlet L-functions for real characters. For tables of dilogarithms, polylogarithms, and Clausen’s integral see §§22.84–22.858.